Calculation of Approximate Derivative Using Continuous Wavelet Transform
Shao‐Wei Xue · Jisuanji yu yingyong huaxue · 2000
A novel method based on continuous wavelet transform (CWT) with Haar wavelet is proposed for approximate derivative calculation. An approximate nth derivative of an analytical signal can be obtained by applying n times of the wavelet transform to the signal. The results obtained from three different methods—the conventional numerical differentiation, the discrete wavelet transform method and the proposed continuous wavelet transform method were compared, it was demonstrated that the results are similar for signals without noise, but the signal to noise ratio (SNR) of the result obtained by the CWT method is improved greatly comparing with the former two methods for noisy signals. The proposed CWT method is an efficient tool for the derivative calculation of analytical signals, especially for signals whose SNR is relatively small.